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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
Find the sum of the first 30 terms, \(s_{30}\), for the arithmetic sequence with first term \(a_{1}=-4\) and common difference \(d=3.5\).
Jem makes a stack of 5 pennies. Each day, Jem adds three pennies to the stack. How many pennies are in the stack after 10 days?
Determine the common ratio of the following geometric sequence: \(\{6,18,54,162, \ldots\}\).
Find the 6th term, \(c_{6}\), of the geometric sequence with \(c_{1}=400\) and \(r=0.25\).
Find the sum of the first 12 terms, \(s_{12}\), for the geometric sequence with first term \(a_{1}=-4\) and common ratio \(r=-1.25\).
Carolann and Tyler deposit \(\$ 8,500\) in an account bearing \(5.5 \%\) interest compounded yearly. If they do not deposit any more money in that account, how much will be in the account after 15 years?
The total number of ebooks sold in 2013 was 242 million \(\left(a_{1}=242\right)\). Each year, the number of ebooks sold has declined by \(3 \%(r=0.97)\). How many ebooks were sold between 2013 and 2022?
\(\{3,7,11,15,25,100, \ldots\}\)Determine if the sequence is a geometric sequence.
\(\{2,4,8,16,32, \ldots\}\)Determine if the sequence is a geometric sequence.
\(\{9,0.9,0.09,0.009,0.00009, \ldots\}\)Determine if the sequence is a geometric sequence.
\(\{262,144,65,536,16,384,4,096,1,024, \ldots\}\)Determine if the sequence is a geometric sequence.
\(\{14,19,24,29,34,50,60\}\)Determine if the sequence is a geometric sequence.
\(\{3.9,2.3,0.7,-0.9,-2.5,-4.1,-5.7, .\).Determine if the sequence is a geometric sequence.
\(\{4,-8,16,-32,64,-128,256, \ldots\}\)Determine if the sequence is a geometric sequence.
\(\{8,-4,2,-1,0.5,-0.25,0.125,-0.0625, \ldots\}\)Determine if the sequence is a geometric sequence.
\(\{3,6,12,24,48,96, \ldots\}\)The sequences given are geometric sequences. Determine the common ratio for each.
\(\{8,24,72,216,648,1944, \ldots\}\)The sequences given are geometric sequences. Determine the common ratio for each.
\(\{15,3,0.6,0.12,0.024,0.0048,0.00096, \ldots\}\)The sequences given are geometric sequences. Determine the common ratio for each.
\(\{52,26,13,6.5,3.25,1.625,0.8125,0.40265 \ldots\}\)The sequences given are geometric sequences. Determine the common ratio for each.
\(\{18,-18,18,-18,18-18, \ldots\}\)The sequences given are geometric sequences. Determine the common ratio for each.
\(\{48,-12,3-0.75,0.1875,-0.046875, \ldots\}\)The sequences given are geometric sequences. Determine the common ratio for each.
\(a_{1}=5, r=3\), find \(a_{6}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(b_{1}=7, r=9\), find \(b_{5}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(c_{1}=11, r=4\), find \(c_{12}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(a_{1}=2, r=7\), find \(a_{9}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(t_{1}=100, r=\frac{1}{5}\), find \(t_{10}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(b_{1}=56, r=0.25\), find \(b_{15}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(b_{1}=13, r=-2\), find \(b_{10}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(a_{1}=11, r=-3\), find \(a_{12}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(a_{1}=12, r=-\frac{1}{3}\), find \(a_{8}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(a_{1}=100, r=-10\), find \(a_{15}\).The first term and the common ratio of a geometric sequence is given. Using that information, determine the indicated term of the sequence.
\(a_{1}=3, r=4\), calculate \(s_{5}\).The first term and the common ratio is given for a geometric sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=5, r=3\), calculate \(s_{9}\).The first term and the common ratio is given for a geometric sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=4, r=5\), calculate \(s_{8}\).The first term and the common ratio is given for a geometric sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=48, r=2\), calculate \(s_{11}\).The first term and the common ratio is given for a geometric sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=450, r=0.5\), calculate \(s_{12}\).The first term and the common ratio is given for a geometric sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=300, r=0.25\), calculate \(s_{10}\).The first term and the common ratio is given for a geometric sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=3, r=-2\), calculate \(s_{11}\).The first term and the common ratio is given for a geometric sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=5, r=-4\), calculate \(s_{8}\).The first term and the common ratio is given for a geometric sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
Lactobacilius acidophilus (L. acidophilus) is a bacterium that grows in milk. In optimal conditions, its population doubles every 26 minutes. If a culture starts with 20 L. acidophilus bacteria, how many bacteria will there be after 390 minutes? This means the 26 -minute time period has occurred 15
Bacillus megaterium (B. megaterium) is a bacterium that grows in sucrose salts. In optimal conditions, its population doubles every 25 minutes. If a culture starts with \(30 \mathrm{~B}\). megaterium bacteria, how many bacteria will there be after 1,000 minutes?Apply your understanding of geometric
Alex and Jill deposit \(\$ 4,000\) in an account bearing \(5 \%\) interest compounded yearly. If they do not deposit any more money in that account, how much will it be worth in 30 years?Apply your understanding of geometric sequences to real-world applications.
Kerry and Megan deposit \(\$ 6,000\) dollars in and account bearing \(4 \%\) compounded yearly. If they do not deposit any more money in that account, how much will be in the account after 40 years?Apply your understanding of geometric sequences to real-world applications.
You decide to color a square that measures \(1 \mathrm{~m}\) on each side in a very particular manner. You first cut the square in half vertically. You color one side of the square with purple. On the side of the square that was not colored, you draw a line dividing that region horizontally exactly
Consider the geometric sequence with first term 0.9 and common ratio of 0.1 . What is the sum of the first 5 terms?Apply your understanding of geometric sequences to real-world applications.
Repeat Exercise 38, for the sum of the first 10 terms.Apply your understanding of geometric sequences to real-world applications.Data from Exercises 38Consider the geometric sequence with first term 0.9 and common ratio of 0.1 . What is the sum of the first 5 terms?
Returning to Kerry and Megan (Exercise 36), what would their account be worth if their account was compounded monthly?Recall that the formula for interest compounded yearly is \(A=P(1+r)^{t}\), where \(A\) is the amount in the account after \(t\) years, \(P\) is the initial amount deposited, and
Returning to Alex and Jill (Exercise 35), what would their account be worth if their account was compounded monthly?Recall that the formula for interest compounded yearly is \(A=P(1+r)^{t}\), where \(A\) is the amount in the account after \(t\) years, \(P\) is the initial amount deposited, and
Imagine your family tree. You have two parents. Your parents have two parents: your grandparents. And so on. How many great-great-great-great-grandparents do you have? Hint: This would be six generations back.Recall that the formula for interest compounded yearly is \(A=P(1+r)^{t}\), where \(A\) is
Imagine your family tree. You have two parents. Your parents have two parents: your grandparents. And so on. How many great (20 times) grandparents do you have? Hint: This would be 22 generations back.Recall that the formula for interest compounded yearly is \(A=P(1+r)^{t}\), where \(A\) is the
\(\{3,7,11,15,25,100, \ldots\}\)Determine if the sequence is an arithmetic sequence.
\(\{27,24,21,18,15,12,9, \ldots\}\)Determine if the sequence is an arithmetic sequence.
\(\{6,-1,-8,-15,-23,-31,-39, \ldots\}\)Determine if the sequence is an arithmetic sequence.
\(\{-5,4,13,22,31,40,49,58,67, \ldots\}\)Determine if the sequence is an arithmetic sequence.
\(\{14,19,24,29,34,50,60\}\)Determine if the sequence is an arithmetic sequence.
\(\{3.9,2.3,0.7,-0.9,-2.5,-4.1,-5.7, \ldots\}\)Determine if the sequence is an arithmetic sequence.
\(\{4,-8,12,-16,20,-24,28,-32, \ldots\}\)Determine if the sequence is an arithmetic sequence.
\(\{1,2,3,5,8,13,21,34,55, \ldots\}\)Determine if the sequence is an arithmetic sequence.
\(\{18,68,118,168,218,268, \ldots\}\)The sequences given are arithmetic sequences. Determine the constant difference for each sequence. Verify that each term is the previous term plus the constant difference.
\(\{13,35,57,79,101,123,145,167, \ldots\}\)The sequences given are arithmetic sequences. Determine the constant difference for each sequence. Verify that each term is the previous term plus the constant difference.
\(\{14,11,8,5,2,-1,-4, \ldots\}\)The sequences given are arithmetic sequences. Determine the constant difference for each sequence. Verify that each term is the previous term plus the constant difference.
\(\{4.5,1.9,-0.7,-3.3,-5.9, \ldots\}\)The sequences given are arithmetic sequences. Determine the constant difference for each sequence. Verify that each term is the previous term plus the constant difference.
\(\{-27,-13,1,15,29,43,57,71, \ldots\}\)The sequences given are arithmetic sequences. Determine the constant difference for each sequence. Verify that each term is the previous term plus the constant difference.
\(\{3.8,10.6,17.4,24.2,31,37.8,44.6, \ldots\}\)The sequences given are arithmetic sequences. Determine the constant difference for each sequence. Verify that each term is the previous term plus the constant difference.
\(a_{1}=12, d=11\), find \(a_{20}\).The first term and the constant difference of an arithmetic sequence is given. Using that information, determine the indicated term of the sequence.
\(b_{1}=5, d=8\), find \(b_{38}\).The first term and the constant difference of an arithmetic sequence is given. Using that information, determine the indicated term of the sequence.
\(c_{1}=48, d=-7\), find \(c_{50}\).The first term and the constant difference of an arithmetic sequence is given. Using that information, determine the indicated term of the sequence.
\(a_{1}=110, d=-16\), find \(a_{27}\).The first term and the constant difference of an arithmetic sequence is given. Using that information, determine the indicated term of the sequence.
\(t_{1}=15.3, d=4.2\), find \(t_{17}\).The first term and the constant difference of an arithmetic sequence is given. Using that information, determine the indicated term of the sequence.
\(b_{1}=23.8, d=11.7\), find \(b_{120}\).The first term and the constant difference of an arithmetic sequence is given. Using that information, determine the indicated term of the sequence.
\(b_{1}=27.45, d=-3.67\), find \(b_{40}\).The first term and the constant difference of an arithmetic sequence is given. Using that information, determine the indicated term of the sequence.
\(a_{1}=67.4, d=-12.3\), find \(a_{200}\)The first term and the constant difference of an arithmetic sequence is given. Using that information, determine the indicated term of the sequence.
\(a_{5}=27, a_{15}=77\)Two terms of an arithmetic sequence are given. Using that information, identify the first term and the constant difference.
\(b_{10}=47, b_{25}=137\)Two terms of an arithmetic sequence are given. Using that information, identify the first term and the constant difference.
\(a_{9}=38, a_{45}=189.2\)Two terms of an arithmetic sequence are given. Using that information, identify the first term and the constant difference.
\(a_{6}=43, a_{41}=-377\)Two terms of an arithmetic sequence are given. Using that information, identify the first term and the constant difference.
\(a_{4}=-12.3, a_{54}=-106.5\)Two terms of an arithmetic sequence are given. Using that information, identify the first term and the constant difference.
\(a_{12}=45.9, a_{60}=-563.7\)Two terms of an arithmetic sequence are given. Using that information, identify the first term and the constant difference.
\(a_{1}=15, d=7\), calculate \(s_{10}\)The first term and the constant difference is given for an arithmetic sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=2, d=13\), calculate \(s_{20}\).The first term and the constant difference is given for an arithmetic sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=105, d=0.3\), calculate \(s_{15}\).The first term and the constant difference is given for an arithmetic sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=56.2, d=1.1\), calculate \(a_{35}\).The first term and the constant difference is given for an arithmetic sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=450, d=-20\), calculate \(s_{20}\).The first term and the constant difference is given for an arithmetic sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
\(a_{1}=1400, d=-35\), calculate \(s_{40}\).The first term and the constant difference is given for an arithmetic sequence. Use that information to find the sum of the first \(n\) terms of the sequence, \(s_{n}\).
A collection is taken up to support a family in need. The initial amount in the collection is \(\$ 135\). Everyone places \(\$ 20\) in the collection. When the 35th person puts their \(\$ 20\) in the collection, how much is present in the collection?Apply your knowledge of arithmetic sequences to
There are 50 songs on a playlist. Every minute, 3 more songs are added to the playlist. How many songs are on the playlist after 40 minutes have passed?Apply your knowledge of arithmetic sequences to these real-world scenarios.
One genre on Netflix has 1,000 shows. Every week, 20 shows are added to that genre. After 15 weeks, how many shows are in that genre?Apply your knowledge of arithmetic sequences to these real-world scenarios.
A new local band has 10 people come to their first show. News of the band spreads afterwards. Each week, 4 more people attend their show than the previous week. After 50 weeks, how many people are at their show?Apply your knowledge of arithmetic sequences to these real-world scenarios.
The Jester Comic book store is going out of business and is taking in no new inventory. Its inventory is currently 13,563 titles. Each day after, they sell or give away 250 titles. After 15 days, how many titles are left?Apply your knowledge of arithmetic sequences to these real-world scenarios.
Jasmyn has decided to train for a marathon. In week one, Jasmyn runs 5 miles. Each week, Jasmyn increased the running distance by 2 miles. How many miles will Jasmyn run in week 13 of the training schedule?Apply your knowledge of arithmetic sequences to these real-world scenarios.
A 42-gallon bathtub sits with 14 gallons in it. The faucet is turned on and is now being filled at the rate of 2.2 gallons per minute, but is draining slowly, at 1.8 gallons per minute. After 20 minutes, how many gallons are in the tub?Apply your knowledge of arithmetic sequences to these
A trained diver is 250 feet deep. The diver is nearly out of air and needs to surface. However, the diver can only comfortably ascend 30 feet per minute. How deep is the diver after ascending for 5 minutes?Apply your knowledge of arithmetic sequences to these real-world scenarios.
Jaclyn, an investor, begins a start-up to revitalize homes in South Bend, Indiana. She begins with \(\$ 10,000\), making her investor 1. Each investor that joins will invest \(\$ 500\) more than the previous investor. How much does the 50th investor invest in the project? With that 50th investor,
Jasmyn has decided to train for a marathon. In week one, Jasmyn runs 5 miles. Each week, Jasmyn increased the running distance by 2 miles. After training for 14 weeks, how many total miles will Jasmyn have run?Apply your knowledge of arithmetic sequences to these real-world scenarios.
The base of a pyramidal structure has 144 blocks. Each level above has 5 fewer blocks than the previous level. How many total blocks are there if the pyramidal structure has 25 levels?Apply your knowledge of arithmetic sequences to these real-world scenarios.
As part of a deal, a friend tells you they will give you \(\$ 10\) on day \(1, \$ 20\) on day \(2, \$ 30\) on day 3 , for all 30 days of a month. At the end of that month, what is the total amount your friend has given you?Apply your knowledge of arithmetic sequences to these real-world scenarios.
Identify which of the following numbers are prime and which are composite. \(31,56,213,48,701\)
Find the prime factorization of 4,570 .
Find the greatest common divisor of 410 and 144 .
Find the least common multiple of 45 and 70 .
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